Question

find the quotient.
$(x^3 + 27) \div (x + 3)$

$(x^3 + 27) \div (x + 3) = \square$
(simplify your answer.)

Explanation:

Step1: Recognize the sum of cubes

The expression \(x^3 + 27\) can be written as a sum of cubes. Recall that \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(a = x\) and \(b = 3\) (since \(3^3=27\)), so \(x^3+27=(x + 3)(x^2-3x + 9)\).

Step2: Divide the factored form by \((x + 3)\)

We have \(\frac{(x + 3)(x^2-3x + 9)}{x + 3}\). The \((x + 3)\) terms in the numerator and denominator cancel out (assuming \(x
eq - 3\)), leaving us with \(x^2-3x + 9\).

Answer:

\(x^2 - 3x + 9\)